File the widened ‘polarization tip’ off the one prong of the plug so it’ll plug into the old 220 V. British (round prong) tip adaptor. Use the brown extension cord not only to bring the electric closer to you (in rooms that only have 1 plug for the whole room), but also to multiply the plug so you can charge your devices along with those of your roommate. :-) Many rooms will have only one plug.
So will a typical extension cord designed for an American 110 volt system be robust enough to handle 220 volts? I find extension cords in 220-volt countries to be thicker. I’ve also found that my thinner extension cords grow hot (scary) when running power-hungry things like drills or hair dryers.
What do I need to look out for?
The thinner cord is fine for low-power devices, but (as you found) may be an issue for more power-hungry devices.
I find it handy to have an extension in airports when charging devices, instead of struggling to sit on the floor next to a plug or stand at a charging station!